Is it compulsory to follow a Madhhab? Is it permissible to transfer from a Madhab to another Madhab?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Allah has not prescribed on us to follow a given Fiqh school. But Allah has made it obligatory on any normal person (not a scholar) to ask a scholar whom he trusts as far as religious matters are concerned and act accordingly. Allah Says (interpretation of meaning): {So ask of those who know the Scripture [learned men of the Taurât (Torah) and the Injeel (Gospel)], if you know not.}[16: 43].
So, there is no harm in your transferring from a Fiqh school to another. (From Shafi to Hambali for instance). In fact, the opinions of both Ahmad's and Shafi's schools are all based on evidence from the Sharia. But some opinions are more preponderant than others. Know also that many scholars changed from one school of Fiqh to another. Imam Al-Tahawi was Shafi then he became Hanafi, … etc.
We would also like to remind you that "Salafia" is not a school of Fiqh, it is a movement that tries to revive many of the practical and scientific religious matters which were neglected due to the blind extremism and inertia of some of the followers of the different Fiqh schools. "Salafia" for instance calls for opening the door of Ijtihad with its criteria and boundaries. So, "Salafia" is a reforming movement of the Fiqh in general and not a different school.

Allah knows best.